Titanium Backup is the most powerful backup tool on Android, and then some. You can backup, restore, freeze (with Pro) your apps + data + Market links. This includes all protected apps & system apps, plus external data on your SD card. You can do 0-click batch & scheduled backups. Backups will operate without closing any apps (with Pro). You can move any app (or app data) to/from the SD card. You can browse any app's data and even query the Market to see detailed information about the app.

Also see the paid Pro key which adds even more awesome features such as:

0-click batch restores

Keep multiple backups per app

Backup/Restore SMS, MMS, calls, bookmarks, WiFi AP as XML

Multi-user app data

Apps freezer

Sync to/from Dropbox (manual/scheduled)

Sync to/from Box (manual/scheduled)

Sync to/from Google Drive (manual/scheduled)

Convert user apps to system apps and vice-versa

Integrate system app updates into ROM

Encryption

Market Doctor (relink apps to Market)

"Destroy all Market links" feature

Hypershell speed

Backup apps without closing them!

Restore individual apps+data from non-root ADB backups!

Restore individual apps+data from CWM backups!

Restore individual apps+data from TWRP backups!

Market "auto updating" manager

Dalvik cache cleaner

Integrate Dalvik cache system elements into ROM

Unlimited schedules

Load/Save a Filter and use it in Widgets/Schedules

Change the device's Android ID, restore it from a backup or after a factory reset

Protect backup against deletion

Send backup (to e-mail/cloud) and import it in 1 click

Backup → Verify → Uninstall an app in one shot

Freeze/Defrost/Launch apps in a single click

CSV export any app DB (e-mail or Google Docs)

Convert app data to/from fast WAL format

Way more!

INSTALLATION INSTRUCTION

Install and run! Note: Remove com.keramidas.TitaniumBackup.odex in /data/app if you used Lucky Patcher to patch Titanium Backup.